ANDREW VAZSONYI, Feature Editor, McLaren School of Business,
University of San Francisco

Paul Erdös, Beloved Math Genius, Leaves Us

by Andrew Vazsonyi, Feature Editor

Last September I began circulating the following stories about Paul Erdös, one of the great mathematicians of this century, and a close personal friend, who died on September 20, 1996, in Warsaw. Since then I've heard from many other friends and colleagues. I don't believe there has been another mathematical genius, nay magician, who was loved, and will be missed, by so many. "Pusztulunk, veszunk," Paul Erdös said in his last phone call to me, quoting an Hungarian bard. He meant that all mathematicians, all of us, are slowly leaving, one after the other. He always had a list of the ones who "left" since his last call. Now, sadly, we must add his name to the list.

First Encounter

I was 14 years old when my father called Erdös' father to ask that his son, a prominent student at the University, pay me a visit. On the appointed day, Erdös knocked on the front door of my father's shoe store, which was located in the Octogon, a well-known plaza in Budapest.

"Give me a four digit number," he said.

"2,532," I replied.

"The square is 6,411,024. Sorry, I am getting old and cannot tell you the cube." (He was 17 years old at the time.)

Erdös continued. "How many proofs of the Pythagorean Theorem do you know?"

"One," I said.

"I know 37," he said with a friendly smile. "Did you know that the points of a straight line do not form a denumerable set?" Then he proceeded to demonstrate Cantor's proof of using the diagonal.

After his visit, the sales woman called Erdös a weirdo, saying it was the first time she had ever seen anyone knock on a shop's door before entering.

Little did I know that this was the beginning of a life-long friendship. A few years later, when it came time for me to choose between mathematics or studying engineering at the Technical University, Erdös settled the issue for me. "I'll hide," he said, "and when you enter the gate of the Technical University, I will shoot you."

The Golden Age of Hungarian Mathematics

In the early years of the 20th century, male aliens invaded the earth and, due to the well-known beauty of Hungarian women, they established their base in Budapest. In the years following, an exceptional group of talented and somewhat eccentric geniuses were born. Among them was Paul Erdös (1913).

Erdös devoted his life to mathematics. His parents were both math teachers. They did not send him to public school; rather, they attended to his education themselves. As a child, Erdös was asked, "What is 85 less 88?"

"Three under zero," he answered. The five year-old math genius had already discovered negative numbers.

He was the youngest Hungarian Ph.D. in math (I was the second). He published over 1,400 articles, most of them joint. These joint papers have led to a well-known pecking order among mathematicians. Those at the highest-level have an Erdös number of 1. It means they have written a joint paper with Erdös. If a mathematician has written a paper jointly with an Erdös Number One mathematician, then his/her Erdös number is 2. And so on... It is said that every real mathematician has an Erdös number less than or equal to 5. Albert Einstein's Erdös number was 2. My Erdös number is 1, an honor which I didn't fully appreciate in 1936.

At the time I was living in Budapest, doing research on a classical graph theorem, the K theorem of Euler. Through much hard work I had finally managed to extend the theorem to infinite graphs. But I only had the necessary, not the sufficient, condition. In those days, Erdös and I met almost daily. We took long walks and skated together -- much to my embarrassment. Because of his strange loping walk, people would turn around and stare at Erdös on the sidewalk. When he and I skated, girls would always ask me who the gorilla was. So one day I made the mistake of telephoning Erdös about my discovery of the extension of Euler's theorem. Twenty minutes later he called me back and told me the proof of sufficient condition. My fate was sealed. I had to write a joint paper with him.

The Language of Erdös

During the Horthy dictatorship in Hungary, spies lurked everywhere. As a result, Erdös developed his own private language, which later became accepted by the universal club of mathematicians. The US was always Uncle Sam, and the USSR became Uncle Joe, after Joe Stalin. Communists were on the "long wave length", because that is the wave length of the color red. In Hungary wives referred to their husbands as "my boss." Erdös inverted the term, and wives are "bosses" in the international community of mathematicians. Husbands are "slaves." Giving a math lecture is "preaching." Children were "epsilons," because small quantities in math are often designated by the Greek letter epsilon.

When you make a general estimate of a quantity you use the word "ordo." Erdös was very fond of playing Ping Pong, and one of the worst players in Manchester was Curt Mahler. So when somebody performed very poorly, Erdös would say he played, "Ordo Mahler," which was abbreviated to "OM." His special language was so contagious that when Mahler wanted to use a derogatory term he would say, "He is OM," without having the faintest idea that he was referring to himself.

Any alcoholic beverage was poison. "Give me an epsilon of poison," he used to say. Classical music was "noise." He could not live without it. He was particularly fond of the baroque (Bach, Vivaldi, and Boccherini). God was referred to as the SF (Supreme Fascist). A mathematician who stopped doing math was "dead" -- he died a most ignominious death. My own "death" was caused by events surrounding WWII. However, in 1960 I proved a very difficult theorem in geometry and Erdös told my wife, Laura, "Strange, Vazsonyi is dead, but never lost the touch. Yesterday he found a proof straight from the Big Book'' (i.e., the book of the SF which contained the solutions to all conceivable mathematical problems).

Erdös always found time to talk and play with children. He never failed to stop when he encountered a mother with a baby, or young child, and ask the bewildered mother, "How old is the epsilon?"

Once Erdös began a tale to my young daughter, Bobbi. "Sam and Joe went up the hill to fetch a pail of water..."

Bobbi interrupted him. "Not so, Erdös, it was Jack and Jill."

Working Habits

When Erdös had a grant at the Institute of Advanced Study in Princeton (the home of Albert Einstein), he was criticized because he never "worked." He was either talking to other mathematicians or playing GO, his favorite game. Yet during this time he published more (joint) papers than the rest of the grantees together.

To my knowledge, Erdös never had an office or desk, but his mind worked on math all the time. While eating lunch with him, he might suddenly jump up and run toward the wall. Usually he'd stop within an inch of the wall. (Unfortunately, for a brief time, he developed some physical coordination problems and would smack into the wall.)

Friends

Before Erdös received worldwide recognition as a mathematician, I received a letter from his mother. "What is to become of my son?" she asked. "What is he going to do for money?"

I explained that the ordinary rules of life do not apply to a genius. "He will manage somehow," I said. "Besides, he has unlimited credit with his friends."

Erdös never had a job, a home, a girl friend, checking account, credit card, or automobile. He kept all his possessions in two suitcases. But his mother protected him, his friends numbered in the thousands, and we cared for him during his frequent travels.

Three days prior to Erdös' arrival the phone would start ringing. Callers with heavy accents would ask for him.

"Hello, I am calling from Berlin. I want to talk to Erdös."

"He is not here yet," I would say.

"Where is he?"

"I don't know."

"Why don't you?"

Click.

Of course, when Erdös arrived, you had no life of your own. He could not drive, so you became his private chauffeur. Laura, as all wives, did all the sewing, mending, laundering, and ironing necessary for ordinary human beings. Erdös was also an early riser, but rather than fix his own breakfast, he would wait for Laura to give him his toast, choice of cereal with brown sugar, raisins, nuts, jam, and egg.

Once, Professor Sego of Stanford fame gave a party and Mrs. Sego came to me practically in tears.

"Erdös dropped in three weeks ago and he is still staying with us. I am at the end of my wits."

"No problem," I said. "Tell him to get out."

"I can't do that. We love him, and could not insult him."

"Do what I said. He will not be insulted at all."

An hour later Erdös came to me and asked me to take him to a motel. I played dumb and asked him what happened. He was very nonchalant. "Oh, Mrs. Sego asked me to move out because I stayed long enough."

The last time he visited me in Santa Rosa, he asked me to take him to a travel agent, purchase a ticket to London, and pay for it myself. He told me that Graham would pay me back. I received the check within three days. (Ron Graham is chief scientist at AT&T Labs.)

Hodgepodge

Erdös was particularly generous with mathematicians, setting up grants for those in need. When he "preached" he announced conjectures and offered prizes, sometimes as high as $3,000, for the first to prove or disprove his conjectures. There is a story that he gave a lecture in Tel Aviv and next morning mathematicians stood in line to claim their winnings.

The sum total of his promised grants ran into many thousands of dollars. He was once asked by a newspaper reporter what would happen if all the conjectures were solved at the same time.

"You see," he replied, "this is like a bank. What if all the depositors came in the same morning claiming their money?"

Last Joke

True to his life, Erdös spent his last day at a math conference, dining with mathematicians, in good spirits, as always. His last joke was: "A doctor a day keeps the apples away."

Why did the SF do this to us? We will never know, nor recover from the loss.

from Decision Line / March 1997 / 28(2)
a publication of the Decision Sciences Institute